Did the Lord or Satan move David to number Israel?

Both statements are true, at different levels. The two verses use the same Hebrew verb, sut (H5496), ‘to incite, stir up’. Chronicles names the immediate agent: Satan (the name means ‘adversary’), who stirred David up, most commentators think, to pride in the strength of his army. Samuel names the One who stands behind all events: the Lord, whose anger was already burning against Israel for sins the text does not name, allowed the incitement and used it to bring judgment on the nation.

The book of Job shows the same pattern. Satan afflicts Job, but only within the limits God sets (Job 1:12; 2:6), and Job can say, “the Lord gave, and the Lord hath taken away” (Job 1:21). Satan intends harm; God permits it for his own purpose of judgment or testing. Neither writer suggests that David was forced: once the count was taken his conscience struck him, and he confessed, “I have sinned greatly in that I have done” (2 Samuel 24:10). Keil and Delitzsch read the two passages together in this way: Satan was the tempter through whom the Lord’s judgment came about.

‘An adversary’

In 1 Chronicles 21:1 the Hebrew satan has no article, so some scholars, and the NET Bible, translate ‘an adversary’, and some of them think of a human enemy whose threat moved David to count his fighting men. Most interpreters, including Keil and Delitzsch, take it as Satan himself.